Minimal degenerations for Nakajima quiver varieties.

Gwyn Bellamy (University of Glasgow)

Wednesday 23rd September 16:00-17:00
Maths 311B

Abstract

Nakajima quiver varieties are an important class of varieties in both algebra and algebraic geometry. Minimal degenerations between nilpotent orbit closures were introduced and studied by Kraft-Procesi as part of their classification of nilpotent orbits in classical type whose orbit closure is normal. The analogue of a nilpotent orbit for Nakajima quiver varieties is a symplectic leaf. I'll describe how you can completely classify the minimal degenerations between symplectic leaves. Both the leaves and their degenerations can be described entirely, and very concretely, in terms of the combinatorics of dimension vectors for the associated quiver. The talk will contain many pictures of Hasse diagrams for quiver varieties, which are an effective way to visualise the degenerations. The talk is based on joint work with T. Schedler.  

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